Which term denotes a playful manner that is not meant to be taken seriously?

The term that denotes a playful manner not meant to be taken seriously is "facetious." When someone is being facetious, they often use humor or sarcasm, making light of a situation or offering a comment that is not meant to be taken literally. This playful tone can be found in jokes or in situations where a serious topic is approached with a light-hearted perspective.

The other terms convey different meanings. "Solemn" refers to a serious, earnest demeanor, which is the opposite of a playful manner. "Pensive" describes a state of deep or serious thought, typically associated with being reflective or melancholic, devoid of playfulness. "Genuine" conveys authenticity and sincerity, lacking the playful connotation of facetiousness. Therefore, facetious is the correct choice as it captures that lighthearted aspect.